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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)5555}\\\end{array}
Use the 1^{st} digit 5 from dividend 5555
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)5555}\\\end{array}
Since 5 is less than 55, use the next digit 5 from dividend 5555 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)5555}\\\end{array}
Use the 2^{nd} digit 5 from dividend 5555
\begin{array}{l}\phantom{55)}01\phantom{4}\\55\overline{)5555}\\\phantom{55)}\underline{\phantom{}55\phantom{99}}\\\phantom{55)99}0\\\end{array}
Find closest multiple of 55 to 55. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 55 to get reminder 0. Add 1 to quotient.
\begin{array}{l}\phantom{55)}01\phantom{5}\\55\overline{)5555}\\\phantom{55)}\underline{\phantom{}55\phantom{99}}\\\phantom{55)99}5\\\end{array}
Use the 3^{rd} digit 5 from dividend 5555
\begin{array}{l}\phantom{55)}010\phantom{6}\\55\overline{)5555}\\\phantom{55)}\underline{\phantom{}55\phantom{99}}\\\phantom{55)99}5\\\end{array}
Since 5 is less than 55, use the next digit 5 from dividend 5555 and add 0 to the quotient
\begin{array}{l}\phantom{55)}010\phantom{7}\\55\overline{)5555}\\\phantom{55)}\underline{\phantom{}55\phantom{99}}\\\phantom{55)99}55\\\end{array}
Use the 4^{th} digit 5 from dividend 5555
\begin{array}{l}\phantom{55)}0101\phantom{8}\\55\overline{)5555}\\\phantom{55)}\underline{\phantom{}55\phantom{99}}\\\phantom{55)99}55\\\phantom{55)}\underline{\phantom{99}55\phantom{}}\\\phantom{55)9999}0\\\end{array}
Find closest multiple of 55 to 55. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 55 to get reminder 0. Add 1 to quotient.
\text{Quotient: }101 \text{Reminder: }0
Since 0 is less than 55, stop the division. The reminder is 0. The topmost line 0101 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 101.